Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data (Q2875742)
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scientific article; zbMATH DE number 6328590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data |
scientific article; zbMATH DE number 6328590 |
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Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data (English)
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11 August 2014
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linear degeneracy
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Chaplygin gas equations
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time-like extremal surfaces
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0.9704123
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0.94885504
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0.9414335
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0.9346818
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0.9280429
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The author studies the Goursat problem for first-order quasilinear hyperbolic systems in the angular domain \(t\geq 0\), \(x_1(t)\leq x\leq x_2(t)\), with \(x_i(t)\) being the characteristics. Each characteristic field is assumed to be degenerate. Global existence of a unique classical solution to the problem is proven under the assumption that the boundary values are \(C^1\) bounded but sufficiently small in the BV sense. An application to the global existence an uniqueness of classical solutions of the characteristic boundary value problem for the equation of time-like extremal surfaces in Minkowski space is discussed in detail.
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